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Author : Rüdiger Verführt
Release : 1996-07
Genre : Mathematics
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques by : Rüdiger Verführt
Download or read book A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques written by Rüdiger Verführt. This book was released on 1996-07. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Rudiger Verfurth
Release : 1996-06-11
Genre : Mathematics
Kind : eBook
Book Rating : 958/5 ( reviews)
Book Synopsis A Review of Posteriori Error Estimation & Adaptive Mesh-Refinement Techniques by : Rudiger Verfurth
Download or read book A Review of Posteriori Error Estimation & Adaptive Mesh-Refinement Techniques written by Rudiger Verfurth. This book was released on 1996-06-11. Available in PDF, EPUB and Kindle. Book excerpt: Wiley—Teubner Series Advances in Numerical Mathematics Editors Hans Georg Bock Mitchell Luskin Wolfgang Hackbusch Rolf Rannacher A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques Rüdiger Verfürth Ruhr-Universität Bochum, Germany Self-adaptive discretization methods have gained an enormous importance for the numerical solution of partial differential equations which arise in physical and technical applications. The aim of these methods is to obtain a numerical solution within a prescribed tolerance using a minimal amount of work. The main tools utilised are a posteriori error estimators and indicators which are able to give global and local information on the error of the numerical solution, using only the computed numerical solution and known data of the problem. Presenting the most frequently used error estimators which have been developed by various scientists in the last two decades, this book demonstrates that they are all based on the same basic principles. These principles are then used to develop an abstract framework which is able to handle general nonlinear problems. The abstract results are applied to various classes of nonlinear elliptic partial differential equations from, for example, fluid and continuum mechanics, to yield reliable and easily computable error estimators. The book covers stationary problems but omits transient problems, where theory is often still too complex and not yet well developed.
Author : Rüdiger Verfürth
Release : 2013-04-18
Genre : Mathematics
Kind : eBook
Book Rating : 77X/5 ( reviews)
Book Synopsis A Posteriori Error Estimation Techniques for Finite Element Methods by : Rüdiger Verfürth
Download or read book A Posteriori Error Estimation Techniques for Finite Element Methods written by Rüdiger Verfürth. This book was released on 2013-04-18. Available in PDF, EPUB and Kindle. Book excerpt: Self-adaptive discretization methods are now an indispensable tool for the numerical solution of partial differential equations that arise from physical and technical applications. The aim is to obtain a numerical solution within a prescribed tolerance using a minimal amount of work. The main tools in achieving this goal are a posteriori error estimates which give global and local information on the error of the numerical solution and which can easily be computed from the given numerical solution and the data of the differential equation. This book reviews the most frequently used a posteriori error estimation techniques and applies them to a broad class of linear and nonlinear elliptic and parabolic equations. Although there are various approaches to adaptivity and a posteriori error estimation, they are all based on a few common principles. The main aim of the book is to elaborate these basic principles and to give guidelines for developing adaptive schemes for new problems. Chapters 1 and 2 are quite elementary and present various error indicators and their use for mesh adaptation in the framework of a simple model problem. The basic principles are introduced using a minimal amount of notations and techniques providing a complete overview for the non-specialist. Chapters 4-6 on the other hand are more advanced and present a posteriori error estimates within a general framework using the technical tools collected in Chapter 3. Most sections close with a bibliographical remark which indicates the historical development and hints at further results.
Author : O. C. Zienkiewicz
Release : 2005-05-26
Genre : Technology & Engineering
Kind : eBook
Book Rating : 77X/5 ( reviews)
Book Synopsis The Finite Element Method: Its Basis and Fundamentals by : O. C. Zienkiewicz
Download or read book The Finite Element Method: Its Basis and Fundamentals written by O. C. Zienkiewicz. This book was released on 2005-05-26. Available in PDF, EPUB and Kindle. Book excerpt: The Sixth Edition of this influential best-selling book delivers the most up-to-date and comprehensive text and reference yet on the basis of the finite element method (FEM) for all engineers and mathematicians. Since the appearance of the first edition 38 years ago, The Finite Element Method provides arguably the most authoritative introductory text to the method, covering the latest developments and approaches in this dynamic subject, and is amply supplemented by exercises, worked solutions and computer algorithms.• The classic FEM text, written by the subject's leading authors • Enhancements include more worked examples and exercises• With a new chapter on automatic mesh generation and added materials on shape function development and the use of higher order elements in solving elasticity and field problemsActive research has shaped The Finite Element Method into the pre-eminent tool for the modelling of physical systems. It maintains the comprehensive style of earlier editions, while presenting the systematic development for the solution of problems modelled by linear differential equations. Together with the second and third self-contained volumes (0750663219 and 0750663227), The Finite Element Method Set (0750664312) provides a formidable resource covering the theory and the application of FEM, including the basis of the method, its application to advanced solid and structural mechanics and to computational fluid dynamics. - The classic introduction to the finite element method, by two of the subject's leading authors - Any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in this key text
Author : Ehsan Rabizadeh
Release : 2019
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Goal-oriented A Posteriori Error Estimation and Adaptive Mesh Refinement in 2D/3D Thermoelasticity Problems by : Ehsan Rabizadeh
Download or read book Goal-oriented A Posteriori Error Estimation and Adaptive Mesh Refinement in 2D/3D Thermoelasticity Problems written by Ehsan Rabizadeh. This book was released on 2019. Available in PDF, EPUB and Kindle. Book excerpt:
